Speaker
Description
Solving systems of nonlinear differential equation, such as found in plasma physics, is a current challenge in fault-tolerant quantum computing. To this aim, a method to solve the classical Liouville equation on quantum computers is developed using the Koopman-Von Neumann transform.The quantum algorithm evolves an initial wavefunction in discrete space and time whose probability density evolves according to Liouville equation. The quantum circuit associated to the algorithm mainly requires the Quantum Fourier Transform and diagonal unitaries which are efficiently implementable with Walsh series. The resource requirement is analyzed. To exemplify the method, two Liouville systems are studied using the algorithm: a 1D Harmonic Oscillator to exemplify the method, and the Lokta-Volterra system to explore the algorithm's performance on a non linear system.
